Solved: Homogeneous Functions A function is homogeneous of degree when In Exercises 37
Chapter 13, Problem 38(choose chapter or problem)
A function f is homogeneous of degree n when \(f(t x, t y)=t^{n} f(x, y)\). In Exercises 37-40, (a) show that the function is homogeneous and determine n, and (b) show that \(x f_{x}(x, y)+y f_{y}(x, y)=n f(x, y)\).
\(f(x, y)=x^{3}-3 x y^{2}+y^{3}\)
Text Transcription:
f(tx, ty) = t^n f(x, y)
xf_x (x, y) + yf_y (x, y) = n f(x, y)
f(x, y) = x^3 - 3xy^2 + y^3
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